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This paper presents a quasistatic problem of an elastic body in frictional contact with a moving foundation. The model takes into account wear of the contact surface of the body caused by the friction. We recall existence and uniqueness results obtained in Sofonea et al. (2017). The main aim of this paper is to present a fully discrete scheme for numerical approximation together with an error estimation of a solution to this problem. Finally, computational simulations are performed to illustrate the mathematical model. [ABSTRACT FROM AUTHOR]

Numerical models for vibro-acoustic analyses of complex mechanical systems are becoming more and more popular, in particular in the field of virtual product development. Therefore, reliable, comprehensive, and validated modeling methodologies remain crucial. However, system characteristics such as elasticities of the drive train components and nonlinear characteristics can lead to complex, and costly numerical models with a huge number of degrees of freedom. This may raise not only the need for novel and reasonable modeling strategies, but also exacerbates validation process, due to the wide scope in terms of operating conditions. In practice, structure-borne noise signals, for example, from accelerometers, are often used for the validation of mechanical systems. By choice of a sufficient number of measurement points, the interpretation becomes more complex. A lot of vibration response curves then need to be compared and interpreted over a wide operating range. In general, the interpretation focuses on deviations in quality and quantity. In this paper, to overcome these mentioned challenges, a validation methodology is proposed allowing a fast and transparent check of a number of captured signals. Therefore, it is shown how the original information can be reduced in a meaningful manner, making it possible to run a fast and accurate validation. The method is demonstrated on a real application with high mechanical complexity and it is shown that the chosen parameters are reliable. [ABSTRACT FROM AUTHOR]

Abstract Downburst produces strong winds near the ground and causes severe damage to buildings and people. The non-stationarity of downburst is characterized by moving downdraft and pulsed jet to the ground. In practice, both characteristics have often been observed simultaneously. These characteristics significantly affect the wind loads on buildings, particularly on low-rise buildings. However, the previous experimental studies of downbursts focused on each of these characteristics separately. No study has been made of their coupled effect. Therefore, we have developed a downburst simulator, which can generate a pulsed jet and a moving downdraft either separately or simultaneously. In the present paper, we have experimentally investigated the effects of non-stationary characteristics of downbursts on the wind field and wind loads on a flat-roofed low-rise building using this downburst simulator. The results may become a useful database for validating numerical simulation models of downbursts. Highlights • Effects of movement and impinging jet on the flow field of downburst is investigated. • Non-stationary flow fields of moving and pulsed jet are experimentally reproduced. • Downburst-induced pressure on a building is measured with a downburst simulator. • Downburst-induced wind forces are different from those by turbulent boundary layers. [ABSTRACT FROM AUTHOR]

Numerical schemes provably preserving the positivity of density and pressure are highly desirable for ideal magnetohydrodynamics (MHD), but the rigorous positivity-preserving (PP) analysis remains challenging. The difficulties mainly arise from the intrinsic complexity of the MHD equations as well as the indeterminate relation between the PP property and the divergence-free condition on the magnetic field. This paper presents the first rigorous PP analysis of conservative schemes with the Lax--Friedrichs (LF) flux for 1D and multidimensional ideal MHD. The significant innovation is the discovery of the theoretical connection between the PP property and a discrete divergence-free (DDF) condition. This connection is established through the generalized LF splitting properties, which are alternatives to the usually expected LF splitting property that does not hold for ideal MHD. The generalized LF splitting properties involve a number of admissible states strongly coupled by the DDF condition, making their derivation very difficult. We derive these properties via a novel equivalent form of the admissible state set and an important inequality, which is skillfully constructed by technical estimates. Rigorous PP analysis is then presented for finite volume and discontinuous Galerkin schemes with the LF flux on uniform Cartesian meshes. In the 1D case, the PP property is proved for the first-order scheme with proper numerical viscosity, and also for arbitrarily high-order schemes under conditions accessible by a PP limiter. In the 2D case, we show that the DDF condition is necessary and crucial for achieving the PP property. It is observed that even slightly violating the proposed DDF condition may cause failure to preserve the positivity of pressure. We prove that the 2D LF type scheme with proper numerical viscosity preserves both the positivity and the DDF condition. Sufficient conditions are derived for 2D PP high-order schemes, and extension to 3D is discussed. Numerical examples provided in the supplementary material further confirm the theoretical findings. [ABSTRACT FROM AUTHOR]

The paper has considered the fractal flow in a dual media with fractal properties, where the media could be elastic, heterogeneous and visco-elastic. We argued that, the fractal flow within a geological formation with elastic property cannot be accurately described with the concept of differentiation with local operator, as this operator is unable to include into mathematical formulation the effect of elasticity. Thus to include into mathematical formula the observed facts, we have modified the model by replacing the local derivative with the non-local operator with power. A more complex problem was considered where the geological formation is considered to have visco-elastic and heterogeneity properties. We argued that, the flow within a matrix rock with these two properties cannot either be described with local derivative nor a non-local derivative with power law. In this case two non-local operators were considered, an operator with Mittag-Leffler kernel and Mittag-Leffler-Power law kernel [F. Ali et al., J. Magn. Magn. Mater. 423, 327 (2017); F. Ali et al., Eur. Phys. J. Plus 131, 310 (2016); F. Ali et al., Eur. Phys. J. Plus 131, 377 (2016); F. Ali et al., Nonlinear Sci. Lett. A 8, 101 (2017); N.A. Sheikh et al., Neural Comput. Appl. (2016) https://doi.org/10.1007/s00521-016-2815-5]. For each model, a detailed study of existence and uniqueness of the system solutions was presented using the fixed point theorem. We solved numerically each model using a more acculturate numerical scheme known as Upwind. Some numerical simulations are presented to underpin the effect of the suggested fractional differentiation. [ABSTRACT FROM AUTHOR]

A new class of history-dependent quasivariational inequalities was recently studied in [M. Sofonea and A. Matei, History-dependent quasivariational inequalities arising in contact mechanics. Eur. J. Appl. Math. 22 (2011) 471–491]. Existence, uniqueness and regularity results were proved and used in the study of several mathematical models which describe the contact between a deformable body and an obstacle. The aim of this paper is to provide numerical analysis of the quasivariational inequalities introduced in the aforementioned paper. To this end we introduce temporally semi-discrete and fully discrete schemes for the numerical approximation of the inequalities, show their unique solvability, and derive error estimates. We then apply these results to a quasistatic frictional contact problem in which the material’s behavior is modeled with a viscoelastic constitutive law, the contact is bilateral, and friction is described with a slip-rate version of Coulomb’s law. We discuss implementation of the corresponding fully-discrete scheme and present numerical simulation results on a two-dimensional example. [ABSTRACT FROM AUTHOR]

The capacity to quickly and accurately simulate extracellular stimulation of neurons is essential to the design of next-generation neural prostheses. Existing platforms for simulating neurons are largely based on finite-difference techniques; due to the complex geometries involved, the more powerful spectral or differential quadrature techniques cannot be applied directly. This paper presents a mathematical basis for the application of a spectral element method to the problem of simulating the extracellular stimulation of retinal neurons, which is readily extensible to neural fibers of any kind. The activating function formalism is extended to arbitrary neuron geometries, and a segmentation method to guarantee an appropriate choice of collocation points is presented. Differential quadrature may then be applied to efficiently solve the resulting cable equations. The capacity for this model to simulate action potentials propagating through branching structures and to predict minimum extracellular stimulation thresholds for individual neurons is demonstrated. The presented model is validated against published values for extracellular stimulation threshold and conduction velocity for realistic physiological parameter values. This model suggests that convoluted axon geometries are more readily activated by extracellular stimulation than linear axon geometries, which may have ramifications for the design of neural prostheses. [ABSTRACT FROM AUTHOR]

Shape-memory polymers (SMPs) represent a class of smart materials able to store a temporary shape and to recover the original shape upon an external stimulus, such as temperature. The present paper proposes a three-dimensional finite-strain phenomenological model for thermo-responsive SMPs, which distinguishes between two material phases presenting different properties and is based on a rule of mixtures. The proposed model is motivated by the earlier work of Reese et al. (2010) and it considers several significant material features that had not been addressed in previous phenomenological approaches. Specifically, the model reproduces both heating-stretching-cooling and cold drawing shape-fixing procedures and it takes into account the non-ideal behavior of realistic SMPs (i.e. imperfect shape-fixing and incomplete shape-recovery). Several numerical tests are reported to assess model performances, from simple uniaxial and biaxial tests to complex simulations of biomedical devices. Comparisons with experimental data taken from the literature are also provided to validate the model. The proposed improvements increase the model applicability over a wide range of polymer types and operating conditions. [ABSTRACT FROM AUTHOR]

Abstract: This paper concerns the mathematical and numerical modeling of solidification process of pure metals. Such process takes place without development of “mushy zone”, which very often occurs during solidification of alloys. The model is based on the finite element method (FEM) and takes into account the existence of a sharp solidification front which moves according to time. The paper discusses how to include the conditions of continuity on the moving interface as well as the technique of front tracking based on the level set method (LSM). The paper also presents the results of computer simulations of the solidification process of pure copper. Two in-home solvers for one- and two-dimensional problems were built. Both of them are based on FEM. The correctness of the front tracking technique was checked by comparing the results obtained from 2D simulation to 1D simulation. Furthermore, the final calculation process was done for the two-dimensional area at different temperatures on the boundaries to demonstrate the effectiveness of the solver for a complex shape of the solidification front. [Copyright &y& Elsevier]

Abstract: Stress peening forming is widely used in the aeronautics industry to induce curvatures in wing skins. Most of the investigations of stress peen forming are empirical and experimental. In this paper, a three step numerical model that can simulate this process was developed. First, an implicit Finite Element Analysis (FEA) with ANSYS where a prebending moment along the spanwise direction of the component was performed. Then, an explicit FEA with LS-DYNA simulating shot impacts on the pre-stressed component was executed in order to obtain the resulting stresses inside the component. Finally, an implicit FEA with ANSYS was performed for calculating the arc heights and the curvature radii of the component in chordwise and spanwise directions. Numerical analysis of the process shows that the prebending moments have an influence not only on the residual stress profiles but also on the curvatures of the deformed component in chordwise and spanwise directions. This model was used to establish a relationship between the prebending moment and the resulting arc heights and residual stress profiles. The numerical strategies developed in this paper supply a useful tool for studying and optimizing the stress peening process. [Copyright &y& Elsevier]

Stiffened plates are the most common structural units used in different structural applications ranging from buildings and bridges to ships and offshore structures. The present paper aiming at investigating the influence of using Y-stiffeners profile instead of conventional stiffeners on the load carrying capacity of ship deck panels under vertical hull girder bending moment. ANSYS (Release 15.0) nonlinear finite element software was used to verify the ultimate strength results obtained from applying the International Association Classification Societies-Common Structural Rules (IACS-CSR) on both conventional and novel deck panels. The developed numerical model with conventional stiffeners profile was validated in a good agreement with a benchmark study results included in the International Ship Structures Committee (ISSC). Furthermore, both analytical and numerical simulation results were in good agreement that demonstrates the capability of using IACS-CSR for designing the new stiffeners profile in practical applications. In comparison with the conventional stiffeners profile, the proposed Y-stiffeners resulted in a considerable increase in the panel safety margin to weight (area) ratio and higher ultimate strength. Moreover, the numerical simulations provided that implementing the Y-stiffeners profile can also rise the first yielding stress point of the structural response with nearly the same strain absorption in comparison with T-stiffeners profile. [ABSTRACT FROM AUTHOR]

Abstract: We revisit in this paper the theory of axisymmetric vortex rings in an ideal fluid. The boundary separating the vortex ring from the external (potential) flow is assumed of elliptic shape. For a given distribution of vorticity in the vortex core, we theoretically put into evidence the critical parameter for the existence of non-trivial solutions, thus confirming the numerical observation of Durst et al. [ZAMP 32 (1981) 156]. A sharp estimation of the critical threshold is analytically derived. Theoretical predictions are confirmed by numerical simulations using finite elements. A new numerical algorithm is presented and shown to display better performances compared to previous published algorithms using finite differences. The convergence of the iterative algorithm is proved using the theory of elliptic partial differential equations with discontinuous nonlinearities. [Copyright &y& Elsevier]

Liquid crystal elastomers present features not found in ordinary elastic materials, such as semi-soft elasticity and the related stripe domain phenomenon. In this paper, the two-dimensional Bladon–Terentjev–Warner model and the one-constant Oseen–Frank energy expression are combined to study the liquid crystal elastomer. We also impose two material constraints, the incompressibility of the elastomer and the unit director norm of the liquid crystal. We prove existence of minimiser of the energy for the proposed model. Next we formulate the discrete model, and also prove that it possesses a minimiser of the energy. The inf-sup values of the discrete linearised system are then related to the smallest singular values of certain matrices. Next the existence and uniqueness of the Lagrange multipliers associated with the two material constraints are proved under the assumption that the inf-sup conditions hold. Finally numerical simulations of the clamped-pulling experiment are presented for elastomer samples with aspect ratio 1 or 3. The semi-soft elasticity is successfully recovered in both cases. The stripe domain phenomenon, however, is not observed, which might be due to the relative coarse mesh employed in the numerical experiment. Possible improvements are discussed that might lead to the recovery of the stripe domain phenomenon. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper, a three-dimensional (3D), nonisothermal, multiphysics, two-phase steady state transport model and its efficient numerical methods are systematically studied for a full proton exchange membrane fuel cell (PEMFC) in the sense of efficiency and accuracy. The conservation equations of mass, momentum, species, charge and energy are fully addressed in view of nonisothermality and multiphase characteristics. In addition, from an accurate numerical discretization’s point of view, we present some new formulations for species equations by investigating the interactions among the species. In a framework of the combined finite element-upwind finite volume method, some efficient numerical methods are developed in terms of Kirchhoff transformation for the sake of a fast and convergent numerical simulation. The 3D simulations demonstrate that the convergent solutions can be attained within 80 nonlinear iterations, in contrast to the oscillating and nonconvergent iterations conducted by commercial flow solvers or in-house code with standard finite element/volume methods. Numerical convergence tests are carried out to verify the efficiency and accuracy of our numerical algorithms and techniques. [Copyright &y& Elsevier]

In this paper, four three-node triangular finite element models which can readily be incorporated into the standard finite element program framework are devised via a multi-field variational functional for the bounded plane Helmholtz problem. In the models, boundary and domain fields are independently assumed. The former is constructed by nodal interpolation and the latter comprises nonsingular solutions of the Helmholtz equation. The equality of the two fields are enforced along the element boundary. Among the four devised models, the most accurate one is 1/3 to 1/2 less erroneous than the conventional single-field model in most examples. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents the numerical simulations of thin-walled square hollow steel beams subjected to a uniform transverse blast load. The objectives of the numerical simulations were to gain an insight into the temporal distribution of the global and local deformation and the adiabatic temperature rise in the beams as a result of impulsive loading. Additionally, the finite element predictions using Ls-Dyna are compared to the experimentally observed global and local deformations. The full lengths of the beams were modelled using three material models based on the linear piecewise plasticity material model which incorporated strain hardening, with and without strain-rate hardening and with strain-rate hardening and temperature softening. The blast wave was simulated as a rectangular pressure pulse distributed over the top surface of the beams. Ls-Dyna and the material model used were found to predict the global and local deformation of the beams reasonably well. Incorporating strain-rate hardening was found to be important to be able to predict the global and local deformation of the beams. Thermal softening was found to play a small but not negligible role. [Copyright &y& Elsevier]

In this paper, we present a rigorous numerical analysis for a bounded artificial viscosity model (τ = μδσa(δ∥∇su∥F )∇su) for the numerical simulation of turbulent flows. In practice, the commonly used Smagorinsky model (τ = (csδ)2∥∇su∥F ∇su) is overly dissipative and yields unphysical results. To date, several methods for "clipping" the Smagorinsky viscosity have proven useful in improving the physical characteristics of the simulated flow. However, such heuristic strategies strongly rely upon a priori knowledge of the flow regime. The bounded artificial viscosity model relies on a highly nonlinear, but monotone and smooth, semilinear elliptic form for the artificial viscosity. For this model, we have introduced a variational computational strategy, provided finite element error convergence estimates, and included several computational examples indicating its improvement on the overly diffusive Smagorinsky model. [ABSTRACT FROM AUTHOR]

The time-dependent Ginzburg-Landau model is used extensively in studying the nonequilibrium state of superconductivity. The computer simulation of this model requires highperformance computing power and reliable and efficient numerical methods to solve the GinzburgLandau equations. In this paper, a linearized Crank-Nicolson-Galerkin method is proposed for solving these nonlinear and coupled partial differential equations. The method uses the Galerkin finite element approximation in spatial discretization and the Crank-Nicolson implicit scheme in time discretization, together with certain techniques which linearize and decouple the Ginzburg-Landau equations. While retaining the stability and accuracy of the Crank-Nicolson scheme, the proposed approach results in symmetric and positive definite matrix problems, thus substantially improving the computational efficiency. Furthermore, and even more important, the proposed approach is suitable for large-scale parallel computation. Numerical results from simulating the vortex dynamics of superconductivity by using the linearized Crank-Nicolson-Galerkin method are presented. [ABSTRACT FROM AUTHOR]